What is the domain of f(x)=(x-4)/(ln(x-2)) ?

The domain of f(x)=(x-4)/(ln(x-2)) is 2 3

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domain of f(x)=(x-4)/(ln(x-2))

domain

f (x) = \frac{x - 4}{ln ( x - 2 )}

2 < x < 3 or x > 3

Interval Notation

(2, 3) \cup (3, \infty)

Solution steps

Find positive values for logs:

x > 2

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

2 < x < 3 or x > 3

\frac{a + 10}{a ( a - 1 )} - 1

\frac{- 8 x - 14}{- 8 x ^{2} - 61 x + 24}

f (x) = - 2 x^{2} + 60 x

\frac{x - 1}{( x - 1 ) ( x + 2 )}

f (x) = - 3 cos (\frac{7}{12} π x) + 6

What is the domain of f(x)=(x-4)/(ln(x-2)) ?
The domain of f(x)=(x-4)/(ln(x-2)) is 2<x<3\lor x>3